12.24   A regression was performed using data on 16 randomly selected charities in 2003. The vari- ables were Y = expenses (millions of dollars) and X = revenue (millions of dollars). (a) Write the fitted regression equation. (b) Construct a 95 percent confidence interval for the slope.

(c)  Perform a right-tailed t test for zero slope at α = .05. State the hypotheses clearly. (d) Use Excel to find the p-value for the t statistic for the slope. (Data are from Forbes 172, no. 12,

p. 248, and www.forbes.com.)          Charities

 

 

variables	coefficients	std. error
Intercept	7.6425	10.0403
Revenue	0.9467	0.0936

 

 

 

 

 

               12.25 Below is a regression using X = home price (000), Y = annual taxes (000), n = 20 homes.

(a)  Write the fitted regression equation. (b) Write the formula for each t statistic and verify the

t statistics shown below. (c) State the degrees of freedom for the t tests and find the two-tail criti- cal value for t by using Appendix D. (d) Use Excel’s function =TDIST(t, deg_freedom, tails) to verify the p-value shown for each t statistic (slope, intercept). (e) Verify that F = t 2 for the slope. (f ) In

your own words, describe the fit of this regression.

 

 

 

R2               0.452 Std. Error     0.454 n                12   ANOVA table
Source	SS		df	MS	F	p-value
Regression           1.6941			1	1.6941	8.23	.0167
Residual               2.0578			10	0.2058
Total	3.7519		11
  Regression output			Â	Â	  confidence interval
variables	coefficients	std. error	t (df =10)	p-value	95% lower      95% upper
Intercept	1.8064	0.6116	2.954	.0144	0.4438	3.1691
Slope	0.0039	0.0014	2.869	.0167	0.0009	0.0070